If $${v_e}$$ is escape velocity and $${v_o}$$ is orbital velocity of a satellite for orbit close to the earth's surface, then these are related by

A geostationary satellite is orbiting the earth at a height of 5R above the surface of the earth, R being the radius of the earth. The time period of another satellite in hours at a height of 2R from the surface of the earth is

A spherical planet has a mass M_P and diameter D_P. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity, equal to

The height at which the weight of a body becomes $${\left( {{1 \over {16}}} \right)^{th}}$$, its weight on the surface of earth (radius R), is